Existence and Hyers-Ulam stability of a coupled fractional differential system involving the $${\rm{\Psi\ }}$$-Caputo derivative and mixed boundary conditions

In this study, the Banach contraction principle and Schaefer’s fixed point theorem are employed to establish, respectively, the uniqueness and existence of solutions for a coupled fractional differential system subject to mixed boundary conditions. These conditions consist of Dirichlet conditions and nonlocal fractional integral conditions involving the $$\Psi$$ -Riemann-Liouville fractional integral evaluated at the interior point $$\gamma$$ . Furthermore, the Hyers-Ulam stability of the proposed system is examined. Finally, an illustrative example is provided to support the theoretical findings.